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Author Reingold, Omer
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2008
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Derandomization ♦ Bounded space algorithms ♦ Pseudorandom generator
Abstract We present a $\textit{deterministic},$ log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was $log^{4/3}(ṡ)$ obtained by Armoni, Ta-Shma, Wigderson and Zhou (JACM 2000). As undirected st-connectivity is complete for the class of problems solvable by symmetric, nondeterministic, log-space computations (the class SL), this algorithm implies that SL = L (where L is the class of problems solvable by deterministic log-space computations). Independent of our work (and using different techniques), Trifonov (STOC 2005) has presented an $\textit{O}(log$ $\textit{n}$ log log $\textit{n})-space,$ deterministic algorithm for undirected st-connectivity. Our algorithm also implies a way to construct in log-space a $\textit{fixed}$ sequence of directions that guides a deterministic walk through all of the vertices of any connected graph. Specifically, we give log-space constructible universal-traversal sequences for graphs with restricted labeling and log-space constructible universal-exploration sequences for general graphs.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2008-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 55
Issue Number 4
Page Count 24
Starting Page 1
Ending Page 24


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Source: ACM Digital Library